Size Lumber up to Requirement
First of all you will need to resize lumber and cut it into the sizes you have measured or required for the nook. Remember, you will need a bottom and an upper or top plate. Once you have readied two plates, place studs at a measured distance. A general measurement for distance between two studs is from 16 to 24 inches. The distance can also depend on width of the insulation bats. So, keep that aspect in mind as well.
The next step for you is to build the frame. This is done by nailing down the top lumber plate to the bottom. Be careful about the distance you have measured while nailing down both plates to each other. This distance should remain the same.
After you have built the frame, secure it with adhesive you have bought for the purpose. Run a bead of adhesive along the floor next to the wall, and make sure there is no gap left. Then make pilot holes for masonry screws. Once it is done, attach the frame to the wall.
The next important step is fitting of batting into the frame between the studs. While doing so do not compress insulation too hard, you can risk damaging it. Also make sure not to leave any gaps.
Nail Beadboard to Frame
The final step is to naili the beadboard to the frame, but before you do that, you will have to cut the beadboard into pieces of its size. Once you are done with nailing it to the frame, trimming is the only work left for you and your job is done.